A simplified approach to the damage tolerance design of asymmetric tapered laminates. Part II: Methodology validation

An analytical approach for the computation of the energy release rates associated with ply drop-offs has been presented in Part I of this study; the methodology is based on the Euler–Bernoulli theory applied to layered beams, together with orthotropic rescaling. The analytical approach accounts for both thick and thin section delaminations, as well as for variable tapering angles. This paper presents the validation for the analytical methodology which has been developed in Part I. The validation is carried out via: (1) comparison with finite element solutions in terms of energy release rates versus delamination length; (2) prediction of delamination onset load in experimentally characterized tapered samples under combined tension and bending.     

Low-velocity impact damage on dispersed stacking sequence laminates. Part I: Experiments

The stacking sequence design of composite laminates is often limited to combinations of 0°, 90°, and ±45° fibre angle plies. Furthermore, in order to comply to certain stiffness requirements, clustering of plies becomes unavoidable. Although such laminates might have the desired stiffness properties, they may show poor impact and/or compression-after-impact behaviour.A method to redesign the traditional stacking sequences such that the alternative laminates have improved damage resistance whilst keeping similar in-plane and bending stiffness properties as their original traditional stacking sequences is proposed. This method makes use of optimisation tools based on genetic algorithms. In the alternative laminates, the difference between fibre angles of two consecutive plies is maximised and allowed to vary in the 0–90° fibre angle range at intervals of 5°. Manufacturing of such laminates is practical nowadays as the industry is changing its production techniques into accurate automated fibre-placement and tape-laying technologies. A two-step approach is proposed for the design of laminates. In the first step, the optimal laminate is designed in the traditional fashion to cope with the expected quasi-static loads on the structure. The second step consists of redesigning this laminate to better withstand impact loads by dispersing its stacking sequence while keeping similar stiffness properties as in the first step.A traditional laminate and two dispersed stacking sequence alternative layups were tested under low-velocity impact and compression-after-impact loads in order to compare their impact resistance and damage tolerance characteristics. The evaluation of these laminates will also be carried out by the innovative numerical tools proposed in the follow-up of the present paper.     

A simplified design approach to corbels made with high strength concrete

Design procedures for corbels are given in various Codes of Practice e.g. ACI 318-89 [1]. These codes give equations based on research on corbels made with normal strength concrete. Consequently, they tend to limit the value of concrete strength to be used in these equations. This will result in an underestimation of the load carrying capacity of corbels made with high strength concrete (HSC) as will be shown later. In the present paper, a semi-empirical equation for the design of corbels made with high strength concrete is derived. In the derivation, an empirical factor K is used, the value of which was determined from experimental data based on thirty tests made by Fosteret al. [2]. This factor is assumed to be dependent on the shear span/effective depth ratio a/d. The expression found for K was then used to calculate the theoretical load carrying capacity of corbels made with high strength concrete. Twelve more tests were carried out, in-house, on corbels made with high strength concrete and the experimental results were compared with the theoretical values based on K as obtained from the empirical expression. It was found that the expression for K resulted in good correlation between theoretical and experimental values for the load carrying capacity of corbels made with high strength concrete. Comparison of the ACI Code values was made with both experimental and theoretical data and it was found the Code greatly underestimates the load capacity of corbels made with high strength concrete.     

Low-velocity impact damage on dispersed stacking sequence laminates. Part II: Numerical simulations

This paper is the follow-up on the previous work by the authors on the experimental evaluation of the impact damage resistance of laminates with dispersed stacking sequences. The current work focuses on the evaluation of the impact performance of the tested laminates by innovative numerical methods.Constitutive models which take into account the physical progressive failure behaviour of fibres, matrix, and interfaces between plies were implemented in an explicit finite element method and used in the simulation of low-velocity impact events on composite laminates. The computational effort resulted in reliable predictions of the impact dynamics, impact footprint, locus and size of delaminations, matrix cracks and fibre damage, as well as the amount of energy dissipated through delaminations, intraply damage and friction. The accuracy achieved with this method increases the reliability of numerical methods in the simulation of impact loads enabling the reduction of the time and costs associated with mechanical testing.     

Life-cycle modeling for adaptive and variant design. Part 1: Methodology

Life-cycle modeling for design (LCMD) is a methodology for assessing the life-cycle impacts for a complex product with many individual components starting from initial design phases when few design specifications have been made. The methodology combines life-cycle assessment (LCA) with probabilistic design methods in a way that forecasts attributes of possible final designs yet reduces information needs. Specifically, LCMD is a methodology for generating arrays of design scenarios that communicate the range of designs being considered by a design team, and estimating missing data for those design scenarios. The main contribution to enhancing standard LCA is the incorporation of methods to estimate physical attributes of individual components for various design options and in four analyses for evaluating the arrays of design scenarios. An automotive case study presented in part 2 of this work demonstrates one application of LCMD.     

Acousto-optic photonic crossbar switch. Part I: design

We present the design of a 12 × 12 photonic crossbar interconnection network constructed using a single three-dimensional acousto-optic crystal. Previous crossbars based on bulk acousto-optic cells require multichannel deflectors with one deflector per optical input; in contrast the design presented here angularly multiplexes these independent deflectors into a single-transducer acousto-optic device. A Fourier-optics analysis of an acoustically lossy Bragg deflector is coupled to a momentum-space analysis that permits the derivation of complete design equations for the switch. As a concrete example, the complete design of a 12 × 12 crossbar is presented. Finally, a coupled-mode analysis of the first- and second-order diffractions in the angularly multiplexed Bragg cell reveals the fundamental efficiency bounds of the switching network.     

A finite element approach to anisotropic damage of ductile materials in large deformations Part I: an anisotropic ductile elastic-plastic-damage model

During past decades, many material models using the continuum damage mechanics (CDM) approach have been proposed successfully in the small deformation regime to describe inelastic behaviors and fracturing phenomena of a material. For ductile materials, large deformation takes place at the level of damage appearance. Damage is anisotropic in nature. In this paper, the ductile damage at finite deformations is modeled as an anisotropic tensor quantity. Then, a fourth-order symmetric stress correction tensor is proposed for computationally efficient and easy implementation in the finite element formulations. Consequently, an explicit form of the fourth-order constitutive equations of the proposed elastic-plastic-damage model is derived. Both isotropic and kinematic hardening effects are included in the formulation. The new constitutive model can predict not only the elastic-plastic behaviors, but also the sequential variations of ductile materials. An evaluation of the constitutive and damage evolution equations is presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

A computer-assisted geometric approach to the analysis of the impact of billiard balls. Part I: Ideal impacts

It is shown how some recent general theoretical results on impacts of mechanical systems with unilateral constraints, obtained by means of Differential Geometric Impulsive Mechanics, can be operatively applied to the study of impacts between rigid bodies. The applicability of these geometric techniques is partly discussed for general impacts of rigid bodies. In particular, the general aspects of the algorithm are described and applied to analyze the impacts of two equal billiard balls moving on the plane in all possible ideal situations: when the balls can freely slide or roll on the plane of the billiard and/or between themselves. The use of symbolic-computation software is indispensable to solve the computational difficulties arising because of the high number of degrees of freedom of the system. It allows to obtain explicit expressions for the post-impact linear and angular velocities of the balls, and therefore a complete quantitative and qualitative analysis of any particular ideal impact with assigned pre-impact positions and velocities. The data regarding the usual billiard impact with the object ball at rest are explicitly listed and illustrated.     

Traveling-wave piezoelectric linear motor Part I: the stator design.

A new type of piezoelectric linear motor incorporating a traveling wave has been developed. The linear motor is comprised of a stator and a carriage. The stator design, which consists of a meander-line structure and gear teeth mounted on the meander-line structure, is the focus of this article. The meander-line structure is constructed with bimorph actuators arranged in a line. These actuators are driven by two phased sets of alternating current (ac) in order to generate a traveling wave. The traveling wave is transferred to the gear teeth, by which the carriage is driven. Modeling of the stator is derived by use of a strain energy method. The performance of various materials is evaluated by analytical and experimental methods. The analytical and the experimental results are quite approximate. Modal analysis is investigated using ANSYS. Appropriate modes associated with ultrasonic levels of resonant frequency are selected to obtain desired motion and to enhance the output performance. Surface speed for various applied input voltage are studied and indicate a nearly linear relationship. The stator in combination with the carriage makes up the linear motor.     

A novel beamformer design method for medical ultrasound. Part I: Theory

The design of transmit and receive aperture weightings is a critical step in the development of ultrasound imaging systems. Current design methods are generally iterative, and consequently time consuming and inexact. We describe a new and general ultrasound beamformer design method, the minimum sum squared error (MSSE) technique. The MSSE technique enables aperture design for arbitrary beam patterns (within fundamental limitations imposed by diffraction). It uses a linear algebra formulation to describe the system point spread function (psf) as a function of the aperture weightings. The sum squared error (SSE) between the system psf and the desired or goal psf is minimized, yielding the optimal aperture weightings. We present detailed analysis for continuous wave (CW) and broadband systems. We also discuss several possible applications of the technique, such as the design of aperture weightings that improve the system depth of field, generate limited diffraction transmit beams, and improve the correlation depth of field in translated aperture system geometries. Simulation results are presented in an accompanying paper.     

A multi-objective optimization approach for design of blast-resistant composite laminates using carbon nanotubes

A reliable process for the design of blast-resistance composite laminates is needed. We consider here the use of carbon nanotubes (CNTs) to enhance the mechanical properties of composite interface layers. The use of CNTs not only enhances the strength of the interface but also significantly alters stress propagation in composite laminates. A simplified wave propagation simulation is developed and the optimal CNT content in the interface layer is determined using multi-objective optimization paradigms. The optimization process targets minimizing the ratio of the stress developed in the layers to the strength of that layer for all the composite laminate layers. Two optimization methods are employed to identify the optimal CNT content. A case study demonstrating the design of five-layer composite laminate subjected to a blast event is used to demonstrate the concept. It is shown that the addition of 2% and 4% CNTs by weight to the epoxy interfaces results in significant enhancement of the composite ability to resist blast.     

A review of some damage tolerance design approaches for aircraft structures

Damage tolerance design is becoming a necessity in the design of modern aircraft although its importance was recognized as long as four centuries ago by Leonardo da Vinci. Two decades ago structural design engineers and research workers felt the need of incorporating damage tolerance in the design of aircraft structure. Due to a lack of comprehensive damage tolerance methodology large scale component test results were used to develop empirical damage tolerance methods. Recently, linear elastic fracture mechanics has been used in predicting residual strength and crack growth rates in damaged structure. As a result of these efforts significant developments in cracked structure analytical methodology have been achieved. The recent Air Force requirement to apply linear elastic fracture mechanics approach in damage tolerance design of aircraft structures, warrants and critical review of various approaches. In this paper an attempt has been made to critically review some damage tolerance design approaches and their application to aircraft structures.

The paper consists of three main sections: The first section reviews the residual strength analysis methodology, assumptions and limitations of each method are discussed through a simple example. The second part surveys the various crack propagation laws, including linear and non-linear ranges and spectrum loading effects. In the third and last section, fracture mechanics methodology is applied to several types of built-up structural components under spectrum loading conditions. The comparison of test results and analysis of complex structures indicate that simple methods of fracture mechanics can be applied to find the damage tolerant strength and rate of crack growth.

The review presented in this paper indicates that the majority of work done in development of fracture mechanics analytical methodology has been based on data obtained from small scale laboratory specimens tested under closely controlled conditions of damage and environment. The validity of the methodology for complex structure under complex loading conditions has not been established. Before the results of a fracture mechanics analytical methodology can be accepted with a high degree of confidence many realism factors must be properly accounted for in the analysis.     

A study of fastener pull-through failure of composite laminates. Part 1: Experimental

Of the extensive number of investigations examining mechanically fastened composite joints, all but a few are limited to consideration of in-plane modes of failure. An experimental and numerical investigation of fastener pull-through failure of composite joints has therefore been undertaken. The experimental program included an investigation of the influence fastener head geometry, laminate thickness, stacking sequence and material system have upon the pull-through loading response. Circular specimens were transversely loaded to pre-determined displacements of the fastener, sections through the specimen taken and their failure mechanisms investigated with an optical microscope. Pull-through failure was found to be characterised by substantial internal damage similar to that observed for low-velocity impacted composite panels. Failure is not evident from inspection of the laminate surfaces. Damage is manifested in the form of a conically distributed network of matrix cracking and delaminations extending through-the-thickness from the fastener head outer edge, directed away from the fastener hole. The internal/barely visible nature of failure represents a significant departure from that generally considered to distinguish fastener pull-through failure. The means by which to increase resistance to pull-through failure are discussed. This research constitutes work performed as part of the Cooperative Research Centre for Advanced Composite Structures (CRC-ACS) task on highly loaded joints.     

Structured approach to the design of a production data analysis facility. Part 1: Conceptual design and information requirements

The paper reports research into a workshop-oriented machine and inspection framework for a contemporary metalworking small manufacturing enterprise (SME) that cannot be satisfactorily achieved by the rigid scaled-down versions of software applications employed within larger companies. It identifies a structured approach to the design and conceptualization of a production data analysis framework that is supported by the use of order and manufacturing data. A major feature of the framework is its generic applicability and totally integrated approach to provide rapid manufacturing control from intelligent feedback data from the inspection and manufacturing data analysis activities of manufactured components. This production data analysis approach is formally expressed through the combined application of both the activity analysis formalism of IDEF0 and object-oriented information analysis methodology of Booch. The systematic approach employed by the integrated production data analysis framework provides both product and manufacturing process control in order to close the manufacturing feedback loop. These integrated phases are described and involve the concurrent machine operation and inspection planning, simultaneous production code generation, comparative tolerance analysis, and manufacturing data analysis of manufactured components. The final part of the paper provides a critical discussion on a number of major issues of the approach and identifies the advantages and limitations of the research.     

A study of fastener pull-through failure of composite laminates. Part 2: Failure prediction

The experimental study of fastener pull-through failure in composite laminates reported in Part 1 of this paper found pull-through failure to be characterised by substantial internal damage similar to that observed for low-velocity impacted composite panels. Damage is manifested in the form of a conically distributed network of matrix cracking and delaminations extending through-the-thickness from the fastener head outer edge, directed away from the fastener hole. Analysis is conducted in this paper to identify the mechanisms responsible for failure. Finite element analysis indicated high shear stresses at the fastener head outer edge to be responsible for the matrix cracking in this region. Tensile in-plane stresses are the cause of flexural failures found elsewhere in laminates of reduced bending stiffness. Fastener pull-through failure results from the tensile strength of the resin being exceeded. Matrix cracking was found to be the initial mode of failure with cracks aligning themselves perpendicular to the direction of principal stresses. Interply delamination is a secondary mode of failure and represents a propagation of cracking along the path of least resistance. Delaminations are induced due to excessive interlaminar shear and peel strains in the laminate due to through-thickness deformation and matrix cracking respectively. A numerical procedure for the prediction of failure was developed based upon a progressive damage model and a maximum principal strain criterion. Very good correlation between experimental and predicted pull-through failure loads, failure location and failure sequence were achieved. This research constitutes work performed as part of the Cooperative Research Centre for Advanced Composite Structures (CRC-ACS) task on highly loaded joints.     

Characterization and evolution of matrix and interface related damage in [0/90]S laminates under tension. Part I: Numerical predictions

This paper considers damage development mechanisms in cross-ply laminates using an accurate numerical method that assumes a Generalized Plane Strain (GPS) state. A 2D Boundary Element Method (BEM) model is generated to investigate the two types of damage progression in a [0/90]_S laminate: transverse cracks in the 90° lamina and delamination between both laminae. The model permits the contact between the surfaces of the cracks. The study is carried out in terms of the dependence of the Energy Release Rates (ERR) of the two types of crack on their respective lengths. A special emphasis is put on the mechanisms of the joining of the two aforementioned types of crack, including the study of the distribution of the stresses along the interface between the two plies when the transverse crack is approaching this interface.